How to rank players with several statistics of varying importance

Question

I have a database of statistics for the members of our chess club. How do I weight each statistic to be able to rank each player on overall performance? For example, players are tracked by how often they participate in weekly, monthly tournaments. Also, they should be ranked by just showing up, but ranked higher if they show up, and score/win in other categories. They should score higher if the y beat a player ranked higher than they are. And they should be ranked lower as they win over lesser players. But a low-ranked player should not be (overly-) penalyzed for losing to a much higher-ranked player. If a high-ranked player does not show, that would be worse that a similarly high-ranked player losing to 2 or more low-ranked opponents. There are other factors that I want to weight also. I just want to know how to go about establishing weights/formulae in such a scenario based on the importance of each statistic. I hope that's clear.

Answer 1

 A seemingly natural way to do it is to calculate the percent difference between the player rankings,

then split the difference. This is effective in the event of an upset.

 

 For example, suppose player A ranked #35 defeats player B ranked #21.

 

The percent difference is (35-21)/21 = 14/21 = 2/3 = 66 2/3 %

 

So player A improves 33 1/3% in rank while player B falls in rank by the same percentage.

 

That would put player A at 35 * (100% - 33 1/3%) = 35 * 66 2/3 % = 23

 while player B drops to 21 * (100% + 33 1/3 %) = 21 * 1.33333.... = 28

 

 

 

In contrast, an upset by more evenly matched players has less of an effect.

This time, suppose player A, ranked 12 defeats player B ranked 10.

 

The percent difference this time is 20%, so each player improves/declines respectively, by 10%

 

90% of 12 = 10.8 while 10 increased by 10% is 11.

Splitting the decimal points, Player A will be ranked 10th and player B ranked 11.

 

 

The non upset algorithm works similarly but in the opposite direction. A highly ranked player

will not benefit much from defeating a lower ranked player. This can be done by reversing the 

increase/decrease of the percentage above.

 

A no show penalty can be done similarly.

 

Google ranking algorithms for other viable options.